SOLUTION: Hi! A biologist has two brine solutions, one containing 1% salt and another containing 4% salt. How many milliliters of each solution should he mix to obtain 1 L of a solution t

Question 200265: Hi!
A biologist has two brine solutions, one containing 1% salt and another containing 4% salt. How many milliliters of each solution should he mix to obtain 1 L of a solution that contains 2.8% salt?
thanks for the homework help!

Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let

x = amount of brine solution with 1% salt (in liters)
y = amount of brine solution with 4% salt (in liters)

Since he's mixing the two solutions to get one liter, this means that . In other words, the two solutions add up to one liter.

So the first equation is

Since "x" is the amount of the 1% solution, this means that is the amount of pure salt (since 1% of the given solution is given to be salt). Also, is the amount of pure salt (from the other solution). These figures add up to the total (note: 0.028 is the percentage while x+y is the total amount). Now add up the two parts and set them equal to the last portion to get

Start with the given equation.

Distribute

Multiply EVERY number by 1000 (to move the decimal 3 spots to the right)

Get everything to one side

Combine like terms.

So the second equation is

So we have the system of equations:

Multiply the both sides of the first equation by 18.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

------------------------------------------------------------------

Now go back to the first equation.

Plug in .

Multiply.

Multiply both sides by the LCD to clear any fractions.

Distribute and multiply.

Subtract 54 from both sides.

Combine like terms.

Divide both sides by to isolate .

Reduce.

So the solutions are and .

Which form the ordered pair .

These solutions in decimal form are and

Now recall that we stated that the values of "x" and "y" are in units of liters. So this means that x=0.4 liters and y=0.6 liters

Multiply both values by 1000 to convert to milliliters: 1000*0.4=400, 1000*0.6=600

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Answer:

So this means that 400 milliliters of the 1% salt solution and 600 milliliters of the 4% salt solution are needed to make a 1 L solution that is 2.8% salt.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Since the 2 solutions must add to 1 liter, then they must add to 1,000 ml
Let the amount of 1% salt solution in the 2.8% salt solution be x.
Then the amount of 4% solution in the 2.8% salt solution is 1,000 � x

Therefore, we get: .01(x) + .04(1,000 � x) = .028(1,000)

This equation becomes: .01x + 40 - .04x = 28
-.03x + 40 = 28
-.03x = - 12
= 400
Therefore, he needs to mix 400 ML of the 1% salt solution, and 600 (1,000 � 400) ML of the 4% salt solution to get 1,000 ML, or 1 Liter of 2.8% salt solution.

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